A multi-layer mean-field model of the cerebellum embedding microstructure and population-specific dynamics

Mean-field (MF) models are computational formalism used to summarize in a few statistical parameters the salient biophysical properties of an inter-wired neuronal network. Their formalism normally incorporates different types of neurons and synapses along with their topological organization. MFs are crucial to efficiently implement the computational modules of large-scale models of brain function, maintaining the specificity of local cortical microcircuits. While MFs have been generated for the isocortex, they are still missing for other parts of the brain. Here we have designed and simulated a multi-layer MF of the cerebellar microcircuit (including Granule Cells, Golgi Cells, Molecular Layer Interneurons, and Purkinje Cells) and validated it against experimental data and the corresponding spiking neural network (SNN) microcircuit model. The cerebellar MF was built using a system of equations, where properties of neuronal populations and topological parameters are embedded in inter-dependent transfer functions. The model time constant was optimised using local field potentials recorded experimentally from acute mouse cerebellar slices as a template. The MF reproduced the average dynamics of different neuronal populations in response to various input patterns and predicted the modulation of the Purkinje Cells firing depending on cortical plasticity, which drives learning in associative tasks, and the level of feedforward inhibition. The cerebellar MF provides a computationally efficient tool for future investigations of the causal relationship between microscopic neuronal properties and ensemble brain activity in virtual brain models addressing both physiological and pathological conditions

Single whisker representations in the circuitry of the cerebellar cortex

The cerebellum plays a crucial role in sensorimotor processing, yet little is known about its contribution towards sensory signal processing. The whisking behaviour in rodents is a model behaviour for sensorimotor function and the Crus I and II lob ules of the cerebellum have been shown to represent perioral stimulation, linearly encoded whisker setpoint and be important in the generation of whisker movement. To target our investigation of the sensory representation, I have used a very nar rowly defined stimulus, the deflection of a single whisker, to investigate the re sponse in cerebellar cortex neurons using whole-cell and cell-attached patch-clamp. In the first step of cerebellar cortex processing, I found the convergence in individual granule cell of mossy fibre inputs at latencies indicating a direct pathway through the trigeminal nuclei and a cortico-pontine path for the single whisker signal. Mo lecular layer interneurons were found to be highly precisely and rapidly excited by the early direct path input from granule cells. Lateral inhibition was also displayed by a molecular layer interneuron with an inhibitory response. The sole output of the cerebellar cortex, the Purkinje cells, exhibited simple spike responses often combining excitatory and inhibitory phases in the majority of rec orded cells despite the narrowness of the stimulus and the wide recording location. A complex spike response was measured in half of the Purkinje cells with a simple 7 response and never in Purkinje cell without simple spike responses. This separation of the Purkinje cell population into neurons receiving both mossy fibre and climbing fibre input on the single whisker deflection and those that only receive mossy fibre input suggest different mechanisms (e.g. plasticity) and functions. Together, these findings quantify the sensory input to the cerebellar cortex follow ing a single whisker deflection and the downstream processing of this signal.Open Acces

DEVELOPMENT OF A CEREBELLAR MEAN FIELD MODEL: THE THEORETICAL FRAMEWORK, THE IMPLEMENTATION AND THE FIRST APPLICATION

Brain modeling constantly evolves to improve the accuracy of the simulated brain dynamics with the ambitious aim to build a digital twin of the brain. Specific models tuned on brain regions specific features empower the brain simulations introducing bottom-up physiology properties into data-driven simulators. Despite the cerebellum contains 80 % of the neurons and is deeply involved in a wide range of functions, from sensorimotor to cognitive ones, a specific cerebellar model is still missing. Furthermore, its quasi-crystalline multi-layer circuitry deeply differs from the cerebral cortical one, therefore is hard to imagine a unique general model suitable for the realistic simulation of both cerebellar and cerebral cortex. The present thesis tackles the challenge of developing a specific model for the cerebellum. Specifically, multi-neuron multi-layer mean field (MF) model of the cerebellar network, including Granule Cells, Golgi Cells, Molecular Layer Interneurons, and Purkinje Cells, was implemented, and validated against experimental data and the corresponding spiking neural network microcircuit model. The cerebellar MF model was built using a system of interdependent equations, where the single neuronal populations and topological parameters were captured by neuron-specific inter- dependent Transfer Functions. The model time resolution was optimized using Local Field Potentials recorded experimentally with high-density multielectrode array from acute mouse cerebellar slices. The present MF model satisfactorily captured the average discharge of different microcircuit neuronal populations in response to various input patterns and was able to predict the changes in Purkinje Cells firing patterns occurring in specific behavioral conditions: cortical plasticity mapping, which drives learning in associative tasks, and Molecular Layer Interneurons feed-forward inhibition, which controls Purkinje Cells activity patterns. The cerebellar multi-layer MF model thus provides a computationally efficient tool that will allow to investigate the causal relationship between microscopic neuronal properties and ensemble brain activity in health and pathological conditions. Furthermore, preliminary attempts to simulate a pathological cerebellum were done in the perspective of introducing our multi-layer cerebellar MF model in whole-brain simulators to realize patient-specific treatments, moving ahead towards personalized medicine. Two preliminary works assessed the relevant impact of the cerebellum on whole-brain dynamics and its role in modulating complex responses in causal connected cerebral regions, confirming that a specific model is required to further investigate the cerebellum-on- cerebrum influence. The framework presented in this thesis allows to develop a multi-layer MF model depicting the features of a specific brain region (e.g., cerebellum, basal ganglia), in order to define a general strategy to build up a pool of biology grounded MF models for computationally feasible simulations. Interconnected bottom-up MF models integrated in large-scale simulators would capture specific features of different brain regions, while the applications of a virtual brain would have a substantial impact on the reality ranging from the characterization of neurobiological processes, subject-specific preoperative plans, and development of neuro-prosthetic devices

Modeling the Cerebellar Microcircuit: New Strategies for a Long-Standing Issue

The cerebellar microcircuit has been the work bench for theoretical and computational modeling since the beginning of neuroscientific research. The regular neural architecture of the cerebellum inspired different solutions to the long-standing issue of how its circuitry could control motor learning and coordination. Originally, the cerebellar network was modeled using a statistical-topological approach that was later extended by considering the geometrical organization of local microcircuits. However, with the advancement in anatomical and physiological investigations, new discoveries have revealed an unexpected richness of connections, neuronal dynamics and plasticity, calling for a change in modeling strategies, so as to include the multitude of elementary aspects of the network into an integrated and easily updatable computational framework. Recently, biophysically accurate realistic models using a bottom-up strategy accounted for both detailed connectivity and neuronal non-linear membrane dynamics. In this perspective review, we will consider the state of the art and discuss how these initial efforts could be further improved. Moreover, we will consider how embodied neurorobotic models including spiking cerebellar networks could help explaining the role and interplay of distributed forms of plasticity. We envisage that realistic modeling, combined with closed-loop simulations, will help to capture the essence of cerebellar computations and could eventually be applied to neurological diseases and neurorobotic control systems

The Effect of Input from the Cerebellar Nuclei on Activity in Thalamocortical Networks

The cerebellum is a prominent brain structure that contains more than half of all neurons, in the brain, which are densely packed and make up 15% of the total brain mass (Andersen et al., 1992). It is well known for its contribution to the control of motor functions, but it also plays a pivotal role in non-motor behaviours. The cerebellum is also involved in numerous pathological conditions. This thesis contributes to the understanding of the pathophysiology of the cerebello-thalamo-cortical pathways. I concentrate on two cerebellar diseases, namely: absence epilepsy (Noebels, 2005) and downbeat nystagmus (DBN) (Strupp et al., 2007). In this thesis the missing link in explaining the alleviating mechanism of a potassium channel blocker on downbeat nystagmus was found. A simulated single biologically detailed floccular target neuron (FTN) model was stimulated by input from cerebellar Purkinje cells (PCs). It was demonstrated that for both synchronised and unsynchronised input, irregular PC spike trains (which resembles the DBN condition) resulted in elevated FTN firing rates, in comparison with regular (4-AP treated) ones. This increase or decrease of the FTN firing rates during DBN, or after 4-AP treatment, respectively depended on short term depression (STD) at the PC - FTN synapses exclusively in the cases when the PC input was unsynchronised. In contrast, results of previous modelling studies (Glasauer et al, 2011; Glasauer and Rossert, 2008) were not in-line with the corresponding experimental findings (Alvina and Khodakhah, 2010) because they did not take into account the STD on the FTN-PC synapses. It was also demonstrated here that the cerebellar output contributes to the control of absence epilepsy that originates in the thalamocortical network. Moreover, the cerebellar input was most effective when it arrived at the peak of the GSWD burst, with the least effective input arriving during the inter-ictal interval, showing clear phase-dependency. I have also shown that a three-fold increase in the inhibitory time constant, drives the asynchronous-irregular network into an ictal state. This increase reflects the GABAA block. A change to GABAB dominated inhibition results in GSWDs, in which the “wave” component is related to the slow GABAB-mediated K+ currents (Destexhe, 1998). Therefore, in this thesis two important contributions are made to the understanding of cerebellar pathological states: absence epilepsy and DBN, which might in turn be useful in the potential treatment of these conditions.

A New Approach for Determining Phase Response Curves Reveals that Purkinje Cells Can Act as Perfect Integrators

Cerebellar Purkinje cells display complex intrinsic dynamics. They fire spontaneously, exhibit bistability, and via mutual network interactions are involved in the generation of high frequency oscillations and travelling waves of activity. To probe the dynamical properties of Purkinje cells we measured their phase response curves (PRCs). PRCs quantify the change in spike phase caused by a stimulus as a function of its temporal position within the interspike interval, and are widely used to predict neuronal responses to more complex stimulus patterns. Significant variability in the interspike interval during spontaneous firing can lead to PRCs with a low signal-to-noise ratio, requiring averaging over thousands of trials. We show using electrophysiological experiments and simulations that the PRC calculated in the traditional way by sampling the interspike interval with brief current pulses is biased. We introduce a corrected approach for calculating PRCs which eliminates this bias. Using our new approach, we show that Purkinje cell PRCs change qualitatively depending on the firing frequency of the cell. At high firing rates, Purkinje cells exhibit single-peaked, or monophasic PRCs. Surprisingly, at low firing rates, Purkinje cell PRCs are largely independent of phase, resembling PRCs of ideal non-leaky integrate-and-fire neurons. These results indicate that Purkinje cells can act as perfect integrators at low firing rates, and that the integration mode of Purkinje cells depends on their firing rate

Reconstruction and Simulation of a Scaffold Model of the Cerebellar Network

Reconstructing neuronal microcircuits through computational models is fundamental to simulate local neuronal dynamics. Here a scaffold model of the cerebellum has been developed in order to flexibly place neurons in space, connect them synaptically, and endow neurons and synapses with biologically-grounded mechanisms. The scaffold model can keep neuronal morphology separated from network connectivity, which can in turn be obtained from convergence/divergence ratios and axonal/dendritic field 3D geometries. We first tested the scaffold on the cerebellar microcircuit, which presents a challenging 3D organization, at the same time providing appropriate datasets to validate emerging network behaviors. The scaffold was designed to integrate the cerebellar cortex with deep cerebellar nuclei (DCN), including different neuronal types: Golgi cells, granule cells, Purkinje cells, stellate cells, basket cells, and DCN principal cells. Mossy fiber inputs were conveyed through the glomeruli. An anisotropic volume (0.077 mm3) of mouse cerebellum was reconstructed, in which point-neuron models were tuned toward the specific discharge properties of neurons and were connected by exponentially decaying excitatory and inhibitory synapses. Simulations using both pyNEST and pyNEURON showed the emergence of organized spatio-temporal patterns of neuronal activity similar to those revealed experimentally in response to background noise and burst stimulation of mossy fiber bundles. Different configurations of granular and molecular layer connectivity consistently modified neuronal activation patterns, revealing the importance of structural constraints for cerebellar network functioning. The scaffold provided thus an effective workflow accounting for the complex architecture of the cerebellar network. In principle, the scaffold can incorporate cellular mechanisms at multiple levels of detail and be tuned to test different structural and functional hypotheses. A future implementation using detailed 3D multi-compartment neuron models and dynamic synapses will be needed to investigate the impact of single neuron properties on network computation

Excitation and Excitability of Unipolar Brush Cells

__Abstract__ The cerebellum is a distinct brain structure that ensures the spatial accuracy and temporal coordination of movements. It is located superimposed on the brainstem and has an appearance and organization unlike that of the cerebral cortex: its surface has a highly regular foliation pattern, and its neural circuitry is organized in repeated structured modules. Neural activity enters the cerebellum via two excitatory pathways, the mossy ber system and the climbing ber system. Climbing bers originate from the inferior olivary nucleus in the brainstem, and assert a powerful in uence on cerebellar output and long-term adaptation processes. Mossy bers originate from a large number of sources, and carry contextual information on sensory inputs, aspects of motor planning and commands, and proprioceptive feedback. In the cerebellum this information is evaluated and integrated, to produce neural output that in uences ongoing movement directly. Mossy ber signals are processed in the cerebellum in three stages. In the granular layer, the input stage of the cerebellum, mossy ber signals undergo a recoding step where they are combined and expanded by granule cells. Next, in the molecular layer, granule cell signals are integrated with climbing ber signals in Purkinje cells. Together, the granular la